Multiplication of Vectors PYQs: JEE Mains Physics

Showing 1–16 of 16 questions

1. 1. Two particles are located at equal distance from origin. The position vectors of those are represented by \(\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}\) and \(\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}\), respectively. If both the vectors are at right angle to each other, the value of \(\mathrm{n}^{-1}\) is _____ . 2025 Medium
2. 2. A vector has magnitude same as that of \(\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}\) and is parallel to \(\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\). The \(\mathrm{x}\) and \(y\) components of this vector in first quadrant are \(\mathrm{x}\) and \(3\) respectively where  \(x\)= _______. 2024 Hard
3. 3. For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})\), \(\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0\), them value of \(\mathrm{x}\) is _______. 2024 Hard
4. 4. If \(\vec{a}\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5}{9}\right)\) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(n\) is _______. 2024 Hard
5. 5. If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) is 2023 Medium
6. 6. If two vectors \(\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\vec{Q}=4 \hat{i}-2 \hat{j}+ mk\) are perpendicular to each other. Then, the value of \(m\) will be : 2023 Medium
7. 7. Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\) 2023 Hard
8. 8. \(\vec{A}\) is a vector quantity such that \(|\vec{A}|=\) nonzero constant. Which of the following expressions is true for \(\vec{A}\) \(?\) 2022 Easy
9. 9. If \(\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m\) and \(\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m\). The magnitude of component of vector \(\overrightarrow{ A }\) along vector \(\vec{B}\) will be \(......m\). 2022 Medium
10. 10. If the projection of \(2 \hat{i}+4 \hat{j}-2 \hat{k}\) on \(\hat{i}+2 \hat{j}+\alpha \hat{k}\) is zero. Then, the value of \(\alpha\) will be. 2022 Hard
11. 11. If \(\vec{A}\) and \(\vec{B}\) are two vectors satisfying the relation \(\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]\). Then the value of \([\vec{A}-\vec{B}]\). will be : 2021 Medium
12. 12. If \(\overrightarrow{ P } \times \overrightarrow{ Q }=\overrightarrow{ Q } \times \overrightarrow{ P },\) the angle between \(\overrightarrow{ P }\) and \(\overrightarrow{ Q }\) is \(\theta\left(0^{\circ} < \theta < 360^{\circ}\right) .\) The value of \(\theta\) will be ........ 2021 Medium
13. 13. Three particles \({P}, {Q}\) and \({R}\) are moving along the vectors \({A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}\) and \({C}=-\hat{{i}}+\hat{{j}}\) respectively. They strike on a point and start to move in different directions. Now particle \(P\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{B} .\) Similarly particle \(Q\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{C} .\) The angle between the direction of motion of \(P\) and \(Q\) is \(\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)\). Then the value of \(x\) is ...... . 2021 Hard
14. 14. What will be the projection of vector \(A=\hat{i}+\hat{j}+\hat{k}\) on vector \(\vec{B}=\hat{i}+\hat{j}\). 2021 Medium
15. 15. Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) is 2019 Hard
16. 16. Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\)  and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\)  The magnitude of a coplanar vector \(\vec C\) such that  \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by 2018 Hard

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